On Nonparametric Hazard Estimation

[摘要] The Nelson-Aalen estimator provides the basis for the ubiquitous Kaplan-Meier estimator, and therefore is an essential tool for nonparametric survival analysis. This article reviews martingale theory and its role in demonstrating that the Nelson-Aalen estimator is uniformly consistent for estimating the cumulative hazard function for right-censored continuous time-to-failure data.

[关键词] Asymptotic theory;Counting process;Hazard estimation;Martingale theory;Nelson-Aalen estimator;Time-to-failure analysis